Related papers: Realizations of Causal Manifolds by Quantum Fields
The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization…
It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint $4\times 4$ relativistic time operator for…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
Local operators are the basic observables in quantum field theory which encode the physics observed by a local experimentalist. However, when gravity is dynamical, diffeomorphism symmetries are gauged which apparently obstructs a sensible…
Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…
The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…
It can be argued that the ordinary description of the reversible quantum process between two one-to-one correlated measurement outcomes is incomplete because, by not specifying the direction of causality, it allows causal structures that…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time…
The author's attempt to construct a local causal model of quantum theory (QT) that includes quantum field theory (QFT) resulted in the identification of "quantum objects" as the elementary units of causality and locality. Quantum objects…